Chronic, low-level lead poisoning is quite widespread in the United States, causing irreversible neurological problems in children. Assays of blood samples of victims provide data on the amount of lead that is in circulation and not on the accumulated lead concentration in the body which can be determined only by measuring the lead in the skeleton. In vivo measurement of tibia and fingers are commonly used for skeletal lead determination and X-ray fluorescence (XRF) analysis is the accepted method for this purpose. Two methods of XRF are reported in literature, one using lead K x-rays excited by a radioisotope source (K XRF) and the other using lead L x- rays excited by polarized x-rays from an x-ray tube (L XRF). Both methods suffer from larger than desirable minimum detectable concentration. The goal of the proposed research is to improve the minimum detectable limits of these two methods while keeping the radiation dose to the patient as low as possible. Computationally efficient and accurate Monte Carlo simulation would be used to predict the pulse height spectra from samples of known composition and specified geometric configuration for both types of analyzes. The predicted spectra would be verified for accuracy using measured spectra from well- characterized bone phantoms. The code would be used to optimize the design of both systems. The Monte Carlo code would be useful also for calibration of the XRF systems and for determining the minimum detection limits as a function of measurement variables such as the thickness and composition of the overlying tissue. For K XRF analysis, the major thrust would be in increasing the minimum detection limit for lead by careful investigation of several methods including accurate modeling of the source backscatter region of the spectrum and collimation of the source and detector. For L XRF analysis, designs for improving the polarized intensity of the source photons would be studied in order to increase the signal to background ratio under the lead L X-ray peaks. A new analysis principle known as the Monte Carlo-Library Least Squares (MCLLS) principle would be applied to both types of XRF spectra in order to solve the inverse problem of obtaining the amount of lead from the measured spectra. MCLLS is an iterative spectrum analysis algorithm that takes into account all inter-element effects without using correction factors. It also uses all of the information contained in the measured spectrum of the analyte and provides an objective estimate of the variance in the measured concentration.